To determine the whole number unknowns for the solution set of the inequality \( x < y \), we need to analyze what this inequality represents.
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Understanding the Inequality:
- The inequality \( x < y \) means that the value of \( y \) must be greater than the value of \( x \).
- This can be considered in a coordinate system (with \( x \) and \( y \) as axes), where the region of interest is above the line \( y = x \).
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Finding Whole Number Solutions:
- We need to find the pairs of whole numbers (non-negative integers) \( (x, y) \) that satisfy the inequality \( x < y \).
- For whole number solutions, \( x \) can take values from 0 upwards, and for each specific integer value of \( x \), \( y \) must be greater than \( x \).
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Example Solutions:
- If \( x = 0 \), then \( y \) can be \( 1, 2, 3, \ldots \) (i.e., \( y \) can be any whole number greater than \( 0 \)).
- If \( x = 1 \), then \( y \) can be \( 2, 3, 4, \ldots \) (any whole number greater than \( 1 \)).
- If \( x = 2 \), then \( y \) can be \( 3, 4, 5, \ldots \) (i.e., any whole number greater than \( 2 \)).
- This pattern continues indefinitely for all whole numbers.
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Formulating the Solution Set:
- The solution set can be written as pairs \( (x, y) \) such that:
- \( x \) is a whole number \( \geq 0 \)
- \( y \) is a whole number \( > x \)
- The solution set can be written as pairs \( (x, y) \) such that:
Thus, the whole number unknowns for the solution set of the inequality \( x < y \) consist of infinite pairs of whole numbers \( (x, y) \), where for each whole number \( x \), \( y \) must always be greater than \( x \).